Transmission anomalies in 2D photonic crystals from the checkerboard family: from broken to hidden symmetries and plasmon “spoofing”

In a field representation, the main symmetry of the electromagnetic response of complementary metal film structures is described by the Babinet principle, which is expected to be strictly obeyed by structures in vanishingly thin films of a perfect electric conductor. On the other hand, a softer version of this based on transmittance, the transmittance Babinet principle (TBP), is not so restrictive. The goal of this work is to study how severely this broken symmetry affects the optical response of such structures. We consider two geometrically distinct series of planar complementary structures from the checkerboard family: regular and bowtie. The self-complementary structure of these series is known to be very singular and breaks even the rigorous Babinet principle. Here, we study complete simulated transmittance spectral maps (T-Maps), which accumulate the whole spectral response of an entire series of structures in a single plot. The ab initio simulated T-Maps of these 2D photonic crystals were simulated for linearly polarized waves propagating perpendicular to these planar structures, made in a vanishingly thin film of a perfect electric conductor. While we confirm the expected long wavelength validity of the TBP, we show that in the frequency range where diffraction effects dominate, the standard derivation of the TBP no longer applies, and with the help of our T-Maps, we demonstrate a total collapse of the TBP in the structures considered. We show that this broken symmetry practically eliminates all but one transmission band on the hole side of the T-Maps and that the remaining strong band is a "spoof" plasmon, free of multiple frequency replicas, an important feature for optical filter applications. In addition, by symmetry arguments and simulations, we discovered that the T-Maps for bowtie and doubled-period regular structures are identical. We discuss how this hidden symmetry can benefit various applications by providing a convenient scaling, whereby simplified structures can deliver a tailored response.